Quasiperfect domination in triangular lattices

Italo J. Dejter

Discussiones Mathematicae Graph Theory (2009)

  • Volume: 29, Issue: 1, page 179-198
  • ISSN: 2083-5892

Abstract

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A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex ( d v ∈ 1,2 vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol 3,6 and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form K ν , where ν ∈ 1,2,3 depends only on S.

How to cite

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Italo J. Dejter. "Quasiperfect domination in triangular lattices." Discussiones Mathematicae Graph Theory 29.1 (2009): 179-198. <http://eudml.org/doc/270316>.

@article{ItaloJ2009,
abstract = {A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex ($d_v$ ∈ 1,2 vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol 3,6 and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form $K_ν$, where ν ∈ 1,2,3 depends only on S.},
author = {Italo J. Dejter},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {perfect dominating set; quasiperfect dominating set; triangular lattice},
language = {eng},
number = {1},
pages = {179-198},
title = {Quasiperfect domination in triangular lattices},
url = {http://eudml.org/doc/270316},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Italo J. Dejter
TI - Quasiperfect domination in triangular lattices
JO - Discussiones Mathematicae Graph Theory
PY - 2009
VL - 29
IS - 1
SP - 179
EP - 198
AB - A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex ($d_v$ ∈ 1,2 vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol 3,6 and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form $K_ν$, where ν ∈ 1,2,3 depends only on S.
LA - eng
KW - perfect dominating set; quasiperfect dominating set; triangular lattice
UR - http://eudml.org/doc/270316
ER -

References

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  1. [1] D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs, Appl. Discrete Math, eds. R.D. Ringeisen and F.S. Roberts (SIAM, Philadelphia, 1988) 189-199. Zbl0664.05027
  2. [2] I.J. Dejter, Perfect domination of regular grid graphs, Australasian J. Combin. 92 (2008) 99-114. Zbl1153.05042
  3. [3] I.J. Dejter and A.A. Delgado, Perfect dominating sets in grid graphs, JCMCC 70 (2009), to appear. Zbl1195.05053
  4. [4] L. Fejes Tóth, Regular Figures (Pergamon Press, Oxford UK, 1964). 
  5. [5] J. Kratochvil and M. Krivánek, On the Computational Complexity of Codes in Graphs, in: Proc. MFCS 1988, LNCS 324 (Springer-Verlag), 396-404. Zbl0655.68039
  6. [6] C. Thomassen, On the Nelson unit distance coloring problem, Amer. Math. Monthly 106 (1999) 850-853, doi: 10.2307/2589618. Zbl0986.05041

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